REAL-TIME SURVEYINGWITH GPS

Important Phone NumbersTrimble support

Technical Assistance Center ftp://ftp.trimble.comwww.trimble.com

(hardware and software support) 1-800-SOS-4TAC

1-800-767- 4822

Computer Bulletin Board 408-732-6717

System Operator (David Elms) 408-481-6049

Coast Guard Navigation Center www.navcen.uscg.milRecorded message 703-313-5907

Live voice 703-313-5900

Computer Bulletin Board 703-313-5910

National Geodetic Survey www.ngs.noaa.govInformation Center 301-713-3242

Computer Bulletin Board 301-713-4181 or 4182

GPS some background

• Satellite based positioning in development since mid 1960’s

• NAVSTAR GPS• NAVigation Satellite Timing And Ranging

• Global Positioning System

• NAVSTAR GPS - Merging of two military programs in 1973• Naval Research Laboratory - TIMATION program

• Air Force - 621B Project

• Managed by the Department of Defense

• System tested with Ground Transmitters (pseudo-satellites)

• First test satellites (Block I) launched in 1978

• Operational satellites began launching in 1989 (Block II & Block IIA)• Block II & Block IIA launched by Delta II rockets from Cape Canaveral

• Next generation of satellites (Block IIR) are already on contract

GPS the segments

Space Segment

User Segment Monitor StationsDiego Garcia Ascension Is. Kwajalein Hawaii

Control Segment

Colorado Springs

Control / Monitor Segment

• 5 Stations world-wide• Monitored by Department of Defense

• All perform monitor functions• Receive all satellite signals

• Collect Meteorological data ( used for ionospheric modelling )

• Transmit data to MCS

• Master Control Station• Upload to Satellites

• Orbital prediction parameters

• SV Clock corrections

• Ionospheric models

(Basically everything in NAVDATA)

• SV commands

• 25 satellites in final constellation• 6 planes with 55° rotation

• each plane has 4/5 satellites

• Very high orbit• 20,183 KM, 12,545 miles

• approximately 1 revolution in 12 hours

• for accuracy

• survivability

• coverage

Space Segment

Copied from “GPS Navstar User’s Overview” prepare by GPS Joint Program Office, 1984

User Segment

• Surveyors

• Anyone with GPS equipment• Hardware and Software can be application specific

Vehicle Tracking Ambulances

Navigation Police

Mapping Cruise Ships

Hydrographics Courier Services

Aircraft Approach and Landing Hikers

Dredging

Sunken ship salvage

Oil Exploration

A Datum is described by a specifically oriented reference ellipsoid defined by 8 elements

• Position of the network (3 elements)

• Orientation of the network (3 elements)

• Parameters of the reference ellipsoid (2 elements)

Working surfaces

North

AmericaEllipsoid fitting Europe

EuropeEllipsoid fitting North America

Geoid

Regional Datums are designed so that the ellipsoid conforms tothe geoid over the desired region rather than the whole Earth

Earth-Centered, Earth Fixed System

• Z axis = Mean rotational axis (Polar axis)

• X axis = 0 longitude

• X axis in plane of equator• Y axis = 90 E longitude

• Y axis in plane of equator

Elements of an ellipse

• a = semi-major axis b = semi-minor axis

• f = flattening = (a-b)/a

• Parameters used most often: a and 1/f

SEMI-MAJOR AXIS

SEMI-MINOR AXIS

Ellipse in 3-D: an Ellipsoid

SEMI-MAJOR AXIS

SEMI-MINOR AXIS

• Rotate ellipse about semi-minor (polar) axis to obtain 3-d ellipsoid• Semi-major axis is equatorial axis

Common ellipsoids in surveying

• WGS-84 (Datum = WGS-84)

• a = 6378137.000 b = 6356752.310 1/f = 298.2572235630

• GRS-80 (Datum = NAD83)

• a = 6378137.000 b = 6356752.310 1/f = 298.2572221010

• Clarke 1866 (Datum = NAD27)

• a = 6378206.400 b = 6356583.800 1/f = 294.9786982000

• NOTE SIMILARITY BETWEEN WGS-84 AND GRS-80

Datum (WGS 84)

Datum (NAD 27)

Datum

One point can have different sets of coordinates depending on the datum used

x

Z

P

Y

X

Y

X

Z

Coordinate Systems

HCartesian coordinates (X, Y, Z)

Ellipsoidal coordinates (, H)

Altitude Reference

• Ellipsoid• A smooth, mathematically defined model of the earths surface

• Geiod• A surface of equal gravitational pull (equipotential) best fitting the average

sea surface over the whole globe

Geoid

Ellipsoid

HAEMSL Earths Surface

Notes about the geoid

• The geoid approximates mean sea level

• The geoid is a function of the density of the earth

• The geoid is a level surface which undulates

• Conventional levels are referenced to the geoid

Reference Surfaces

Ellipsoid

Earths Surface

Geoid

Ellipsoid Height = H

Height = h

50 ft

84 fth = 73 ft

H = 41 ft

Orthometric

B.M. “A” elevation 84 ft B.M. “ B ” elevation 73 ft

Geoid Height = N

N = 32 ft34 ft

DE = B.M “A” - B.M. “B” =

ORTHOMETRIC 84 ft - 73 ft = 11 ft

ELLIPSOID 50 ft - 41 ft = 9 ft

Conditions for surveying with GPS

• At least 2 receivers required

• At least 4 common SV’s must be tracked from each station

• Visibility to the sky at all stations should be sufficient to track 4 SV’s with good geometry

• Data must be logged at common times (sync rates, or epochs)

• Receivers must be capable of logging carrier phase observables (not just C/A code)

• At some point in the survey, at least one point must be occupied which has known coordinates in the datum and coordinate system desired

• 2 horizontal and 3 vertical control points are required for complete transformation to the desired datum

What the surveyor gets in GPS

• 2 Types of Measurements:• Change in phase of the code

• Change in phase of the carrier wave

• 2 Types of Results:• Single point positioning and navigation -- from code

• Baseline vectors from one station to another (post-processed or processed as “real time”)--from carrier wave

WHAT IS A VECTOR?

Reference

Station1

Vector: Reference to Station1

X

Y

Z

geodesic

on ground distance

Satellite Signal Structure

• Two Carrier Frequencies• L1 - 1575.42 Mhz

• L2 - 1227.6 MHz

• Three modulations• Two PRN codes

• Civilian C/A code L1 -160 dBw Option for L2 in future

• Military P code (Y code if encrypted) L1 -163 dBw L2 -166 dBw

• Navigation message (NAVDATA)

• L1

• L2

• Spread Spectrum

Who uses the code?

• Code-based applications:• Rough mapping

• GIS data acquisition

• Navigation

• Any applications able to tolerate accuracies in range of sub-meter - 5 meters

Measure Ranges to the satellites

• Use the simple formula: Distance = Rate X Time• Distance = RANGE to the satellite (Pseudorange)

• Time = travel time of the signal from the satellite to the user

• When did the signal leave the satellite?

• When did it arrive at the receiver?

• Rate = speed of light

User Time

SV TimeSV Time

How do we know when the signal left the satellite?

One of the Clever Ideas of GPS:

• Use same code at receiver and satellite

• Synchronize satellites and receivers so they're generating same code at same time

• Then we look at the incoming code from the satellite and see how long ago our receiver generated the same code

from satellite

from ground receiver

measure time difference between same part of code

The Integer Ambiguity--What is it?

• Receiver measures partial wavelength when it first logs on

• Receiver counts successive cycles after this

• Receiver does not know whole number of wavelengths behind that first partial one, which exists between the receiver and the SV

• This unknown, N, is called the integer ambiguity or bias (also called phase ambiguity or bias)

How carrier waves produce baselines

• At least 4 common SV’s must be observed from at least 2 separate stations

• The processor uses a technique called “differencing”

• Single difference compares data from 2 SV’s to 1 station, or from 1 SV to 2 stations

• Double difference combines these two types of single differences

• Single and double differences performed at specific epochs in time

• Triple difference combines double differences over successive epochs in time (every 10th epoch normally)

Sequence in processing carrier waves

• Begin with a code estimate of receiver locations

• First generate the triple difference solution

• Based on triple difference processing, find and correct cycle slips

• Using improved estimate of dx,dy,dz from triple difference solution, compute double difference float solution

• Set estimates of N from float solution to integers and re-compute baseline: double difference, fixed integer solution

• Final result of processing is baseline vector, dx,dy,dz, estimated to centimeter-level or better precision

Calculate your position

With range measurments to several satellites you can figure your position using mathematics

• One measurement narrows down our position to the surface of a sphere

11,000 miles

4 unknowns Latitude Longitude Height Time

Need 4 equations

We are somewhereon the surface of this sphere.

Calculate your position cont’d

Second measurement narrows it down to intersection of two spheres

11,000 Miles

12,000 Miles

Intersection of two spheres is a circle

Calculate your position cont’d

Third measurement narrows to just two points

Intersection of three spheres is only two points

In practice 3 measurements are enough to determine a position. We can usually discard one point because it will be a ridiculousanswer, either out in space or moving at high speed.

Calculate your position cont’d

Fourth measurement will decide between the two points.

Fourth measurement will only go through one of the two points

The fourth measurement allows us to solve for the receiver clock bias.

Dilution of precision (DOP)

An indication of the stability of the resulting position

• DOP is dependent upon the geometry of the constellation

• DOP is a magnification factor that relates satellite measurement noise (input) to solution noise (output)

• The lower the DOP, the more accurate the position is.

• The higher the DOP, the less accurate the position is.

• In surveying, we care most about PDOP and RDOP• PDOP = Position dilution of precision--refers to instantaneous SV geometry

• RDOP = Relative dilution of precision--refers to change in SV geometry over the observation period

• For all DOP’s, the lower, the better

Dilution of precision (DOP)

• Relative position of satellites can affect error

idealized situation

4 secs6 secs

Dilution of precision (DOP)

Real situation - fuzzy circles

Point representing position is really a box

4 ‘ish secs6 ‘ish secs

uncertaintyuncertainty

Dilution of precision (DOP)

Even worse at some angles

Area of uncertainty becomes larger as satellites get closer together

Dilution of precision (DOP)

Can be expressed in different dimensions

• GDOP - Geometric dilution of precision

• PDOP - Position dilution of precision

• HDOP - Horizontal dilution of precision

• VDOP - Vertical dilution of precision

• EDOP - East dilution of precision

• NDOP - North dilution of precision

• TDOP - Time dilution of precision• GDOP2 = PDOP2 + TDOP2

• PDOP2 = HDOP2 + VDOP2

• HDOP2 = EDOP2 + NDOP2

Selective Availability (S/A)

Govt. introduces artificial clock and ephemeris errors to throw the system off.

• Prevents hostile forces from using it.

• When turned up, it's the largest source of error

• Selective Availability is the sum of two effects:• Epsilon, or data manipulation term - ephemeris “fibbing”

• Epsilon term changes very slowly - rate change once/hour

• Dither, or clock variations

• Dither term has cyclical variations from 1 cycle every 4 minutes to once every 15 minutes

Error Budget

• Typical observed errors• satellite clocks 2 feet

• ephemeris error 2 feet

• receiver errors 4 feet

• tropospheric/iono 12 feet

• S/A Range error 100 feet

• No S/A Total (rt sq sum) 13 feet• Then multiply by HDOP (usually 2-3) which gives a

total error of:

• typical good receiver 25-40 feet (7-10 meters)

• with S/A Total (rt sq sum) 100 feet• Multiply by HDOP (usually 2-3)

• which gives a total error of:

• typically 200-300 feet (60 to 100 meters)

Feet

S/A

Tropo/Iono

Receivers

Ephemeris

Satellite Clocks

0 20 40 60 80 100

DGPS

• DGPS = “Differential” GPS

• Generally refers to real-time correction of code-based positions

• Real-time capabilities presume radio link between receivers

• The “differential” is the difference between a GPS code position and a known position at a single receiver

Differential Correction

• If you collect data at one location there are going to be errors

• Each of these errors are tagged with GPS time

BASE

Time, t

t+1

.

Differential Correction (Cont.)

• At the same time, the errors occurring at one location are occuring everywhere within the same vicinity

ROVER

Time, t

t+1

?

Differential Correction (Cont.)

1 2 3 4 5 6

BASE

Satellites SeenSatellites Used

1 2 3 4

1 3 5 6 Any Combination of Base SV's

Time, t

t+1

ROVER

Time, t

t+1

? .

GPS Error Sources

• Dilution of Precision (DOP)• Satellite ephemeris removed by differencing• Satellite clock drift removed by differencing• Ionospheric delay removed by differencing• Tropospheric delay removed by differencing• Selective Availability removed by differencing• Multipath• Receiver clock drift• Receiver noise• Unhealthy Satellites

Summary

• 3 Segments of GPS• Space

• Control

• User

• GPS Signals• L1 - c/a code, P-code

• L2 - P-code

• Differentials• Code - sub-meter precision

• Carrier - cm precision

• Integer Ambiguity

Real-Time vs. Post-Processed

• Results are available in the field, so checks can be verified immediately

• Staking out is now possible

• One base receiver supports multiple rovers (unlimited)

• No post-processing time required in office

• Transformation parameters needed prior to survey, for proper relationship between GPS WGS84 and local system

Conditions for Real-Time Surveying

• At least 2 receivers required

• At least 5 common SV’s must be tracked from each station

• Visibility to the sky at all stations should be sufficient to track 5 SV’s with good geometry (4 SV’s required for baseline solution, but 5 are required for initialization)

• Initialization must take place at beginning of survey

• Radio link must be available between base and rover

• “Lock” to SV’s must be maintained, or re-initialization must occur

• Transformation parameters must be available to get from GPS WGS84 LLH to local NEE

What Happens in Real-Time

• Data is logged simultaneously at base and rover

• Base data is transmitted via radio link to radio antenna at rover

• Survey is “initialized” using data from both base and rover (data is processed inside roving receiver)

• Survey is conducted, with processing within roving receiver continuing throughout

• Results of processing are sent to TDC1 for logging and viewing (results normally 2 seconds behind actual reception)

• Results viewed may be either lat/long/ellipsoidal height or northing, easting, elevation, depending on whether sufficient information exists in TDC1 for transformation

What is Initialization?

• Determination of integer wavelength counts up to the satellites

• Required at beginning of all real-time surveys

• Required in the middle of surveys, if continuous tracking of at least 5 SV’s (in common with the base) has been interrupted

Types of Initialization

• Fixed Baseline• Survey Controller (SC) option: “RTK Initializer” (“mini”

fixed baseline)

• SC option: “Known point” -- should be previously surveyed with GPS

• Automatic Initialization• While static -- SC option: “New point”

• While moving -- SC option: “Moving” (often referred to as “OTF”, or on-the-fly)

• NOTE: “Survey Controller” is firmware inside TDC1

Fixed baseline vs. Automatic

• Fixed baseline initialization may be performed with all receivers

• Automatic initialization requires dual frequency receivers (4000 SSE)

• Automatic initialization while moving is additional option to basic 4000SSE real-time configuration

• Survey Controller recognizes capability of receivers in survey, and presents only those options supported by your receivers

Components of RTK system

• BASE• Receiver with RTK firmware -- may be single or dual

frequency; internal memory (GPS data logging capability) not required

• GPS antenna

• TRIMTALK 900 radio

• Radio antenna (7db recommended)

• Battery

• Cables

• 2 Tripods (one for GPS antenna, one for TRIMTALK antenna) and 1 tribrach (radio antenna has mounting bracket with 5/8 thread)

Components of system -- cont.

• ROVER• Receiver -- may be single or dual frequency; internal

memory not required

• RTK firmware

• TDC1 with Survey Controller firmware

• TRIMTALK 900

• GPS antenna

• Radio antenna

• Battery

• Cables

• Recommended: backpack and range pole with bipod

The Radio Link

• Range of TrimTalk 900, with average conditions, is 1-3 km

• Maximum range, with idealconditions, up to 10 km

• Repeaters can be used to extend range

• Base and rovers set on “Reference/Rover”settings

• Repeaters must be set on separate, individual settings

• All radios, including repeaters, must be on same (internal) channel

• One base radio can be received by unlimited rovers

• Rover can receive real-time data from only one base

Real Time Surveying Applications

• Control

• Topographic mapping

• Construction stakeout

• Cadastral surveying

Sources of error in RTS

• Multipath (deflected GPS signal which can give erroneous results -- watch for reflective surfaces in survey area)

• Poor PDOP -- weak satellite geometry (PDOP should be less than 7)

• Erroneous antenna heights

• Interference with radio link -- select a different channel within the TrimTalk

Multipath at Station

Direct Signal

Reflected Signal

Cycle Slips and Loss of Lock

• Cycle slip = interruption of GPS signal, due to:• Obstructions

• Radio or other electromagnetic interference

• Loss of lock = Known integer biases on fewer than 4 SV’s• i.e. Cycle slips on so many SV’s that fewer than 4 integer biases are resolved

• NOTE: if satellite tracking is reduced to 4 SV’s, then resulting PDOP may be too poor (i.e. high) to resolve integer biases on other SV’s -- may require a re-initialization

Grid coordinates

• Initial result of GPS survey is precise network based on (possibly) inaccurate coordinates

• WGS-84 coordinates must be transformed to meaningful local system

• 2 horizontal and 3 vertical control points with values in desired coordinate system and vertical datum are minimum required for transformation

• In RTS, 4-6 control points are minimum number recommended, and up to 10-15 may be desirable for large areas

Grid coordinates -- continued

• Control points are first located with GPS to determine WGS-84 values

• WGS-84 values and known NEE on control points are used to generate proper transformation parameters from GPS system to local grid

• After transformation parameters have been determined (in the office), they are uploaded to TDC1 and used for all subsequent field work, which can now be performed in local grid system

Steps in Calibration

• Locate control points in the field

• Occupy control points using GPS

• Enter control (NEE) and GPS-derived coordinates (WGS-84 LLH) into TRIMMAP

• Perform GPS calibration in TRIMMAP

• Upload results of GPS calibration (by creating a new “DC”, or data collector, file) to TDC1

• Continue field survey, which can now be performed in local grid system

GPS Calibration in TRIMMAP

GPS

WGS84: Latitude, Longitude,and Ellipsoidal Height

Local EllipsoidLocal Latitude, Longitude,

and Ellipsoidal Height

Local Map Projection

Northing, Easting, Height

Local GridNorthing, Easting, Elevation

1 2

3

1 3 or 7 Parameter Datum Transformation (PDT)

2 Projection

3 2D Transformation and Height Adjustment

GPS

WGS84: Latitude, Longitude,and Ellipsoidal Height

Local EllipsoidLocal Latitude, Longitude,

and Ellipsoidal Height

Local Map Projection

Northing, Easting, Height

Local GridNorthing, Easting, Elevation

1 2

3

1 3 or 7 Parameter Datum Transformation (PDT)

2 Projection

3 2D Transformation and Height Adjustment

Another view of GPS Calibration

• CALIBRATION IS 2-STEP PROCESS

• 1. Deriving GPS coordinates for local control points (in the field)

• 2. Computing calibration parameters for the project using TRIMMAP (in the office)

• 4 POSSIBILITIES:

• GPS to LLH on Local Datum: Datum Transformation

• Local LLH to Local NEH: Mapping Projection

• Local NEH to Local NEE: 2-D Transformation

• and Height Adjustment

• NOTE: a Mapping Projection must be selected when creating a project in TRIMMAP, while the remaining three are optional (and will normally be performed)

Summary

• Carrier waves and integer ambiguity

• Real Time Surveys

• Process of the Real Time Surveys

• Initalizations• Fixed

• Automatic

• Components of RTS• Base

• Rover

• Radio